Question

A moving sidewalk in an airport moves people between gates. It takes Jason's 8-year-old

daughter Josie 44 sec to travel 176 ft walking with the sidewalk. It takes her 7 sec to walk 21 ft

against the moving sidewalk in the opposite direction). Find the speed of the sidewalk and find

Josie's speed walking on a non-moving ground.

The side walk moves at Ft/sec

Answer 1

Answer: Josie's speed walking on a non-moving ground is 3.5 ft/sec

The side walk moves at 0.5 Ft/sec

Explanation:

Let x represent Josie's speed walking on a non-moving ground.

Let y represent the speed of the sidewalk.

It takes Jason's 8-year-old daughter Josie 44 sec to travel 176 ft walking with the sidewalk. It means that the total speed at which she moved is

(x + y) ft/sec

Distance = speed × time

Therefore,

176 = 44(x + y)

Dividing both sides by 44, it becomes

4 = x + y- - - - - - - - - - - - - -1

It takes her 7 sec to walk 21 ft against the moving sidewalk in the opposite direction). It means that the total speed at which she moved is (x - y) ft/sec

Therefore,

21 = 7(x - y)

Dividing both sides by 7, it becomes

3 = x - y- - - - - - - - - - - - - -2

Adding equation 1 and 2, it becomes

7 = 2x

x = 7/2 = 3.5 ft/sec

Substituting x = 3.5 into equation 2, it becomes

3 = 3.5 - y

y = 3.5 - 3 = 0.5 ft/sec

Answer 2

The sidewalk moves at 0.5 ft/sec

Josie's speed walking on a non-moving ground is 3.5ft/sec

Explanation:

Let x represent the speed of the side walk and y represent her walking speed

It takes Jason's 8-year-old daughter Josie 44 sec to travel 176 ft walking with the sidewalk

Distance = speed × time

176 = (x+y)×44

44x+44y = 176

x+y = 4 .......1

It takes her 7 sec to walk 21 ft against the moving sidewalk in the opposite direction).

21 = (y-x)7

7y - 7x = 21

y - x = 3 ......2

Add equation 1 to 2

2y = 7

y = 3.5 ft/sec

From equation 1

x + y = 4

x = 4 - 3.5 = 0.5

x = 0.5 ft/sec

The sidewalk moves at 0.5 ft/sec

Josie's speed walking on a non-moving ground is 3.5ft/sec